transformtoPH

◼ transformtoPH[bz, Nph] generates a direct product of basis bz for the fermionic part of the system with a basis for local phonons where Nph is the phonon number cutoff.

◼ transformtoPH works with any basis type. See also qsbasis, qszbasis, qszbasisvc, transformQStoIS.

◼ See also: phononnumber, phononplus, phononminus.

Further examples

Load sneg and declare c to be a Fermionic operator.

<< sneg`sneg`;
snegfermionoperators[c];
snegrealconstants[U, ω, g];

Test basic functionality

transformtoPH[{{{a}, {a1, a2}}, {{b}, {b1}}}, 3] // 
      MatrixForm

Impurity orbital with electron-phonon coupling of the Holstein type

bz = qsbasis[{c[]}];
MatrixForm[bz]

    
Nph = 5;
bzph = transformtoPH[bz, Nph];

    
H = 
      U/2  pow[number[c[]] - 1, 2] + ω phononnumber[Nph] + 
        g phononx[Nph]
mat = makematricesbzop[H, bzph];
showbzmat[mat]